At some point I realized that a lot (maybe most) of the interesting discussions I've had, especially online, ultimately were about a definition. Either making a bad definition clearer, or trying to come to an understanding of a common word with a fuzzy definition. And then once I'd settled on a good definition, the rest of the discussion just kind of fell into place. I also really enjoy defining words in unexpected, but potentially useful (or at least thought provoking) ways, so that's what I'm going to do here.
These definitions aren't going to look like the standard "Websters" or "Wikipedia" definitions. When trying to define a term I think most people's natural instinct is to use the simplest possible words, and also to start big and then "narrow it down." So, to define "cat" we'd get something like: "a small, furry, domesticated, and carnivorous mammal." Which is really the intersection of three groups:
1. Small furry things (for example: lint, mice, cats and dogs. This isn't terribly restrictive)
2. Domesticated animals (every animal that's, usually, not wild. This is pretty restrictive, most animals are wild.)
3. Carnivorous mammals (this is probably the most restrictive group, or best "filter," of the three. Of the things we're likely to run in to everyday, very few of them are carnivorous mammals.)
If we look at the overlap of these three groups (or what makes it through the three filters), it's almost all cats. Although, crucially, there's also going to be a lot of dogs in that group too, which seems like a big failure of this definition. And I think the reason it breaks down is it's a series of increasingly restrictive groups or filters. By the time we get to the last one, if it hasn't uniquely identified "cats" already, the next step will be to add another even more restrictive filter (which would probably get rid of dogs), but that probably wouldn't be enough. We'd probably need another filter to get rid of all the "uncommon" domesticated animals, I'm thinking things like chinchillas or pet pigs.
So, I'm not going to go the traditional route, and these definitions aren't going to look like traditional definitions, at least most of the time. I haven't thought too much about how I'd define "cat", it's not a terribly interesting definition, but it might be something like this: "The most popular domesticated solo-hunting mammal."
This also has three groups, but they're all very broad categories, "domesticated" is probably the smallest of the three and that's a big group. But, even though all three groups are very large, they only overlap in a single case, cats. Of course, that's guaranteed by by using "most popular" (which is kind of cheap shortcut), but even without that, just shortening the definition to "solo-hunting domesticated mammal" probably does as well as a "traditional" definition. And it's because this new definition includes the pretty unusual term "solo-hunting." That's a huge group of animals, but it doesn't overlap in a lot of places with "domesticated" (even though that's also a huge group of animals).
I think that looking at the definition this way, finding a place where a single unique item or group or term, falls at the intersection of two big, broad, but dissimilar groups is a lot more interesting way to approach definitions. It may also be a more accurate way to create a definition in many cases as well. We'll see...